Hey Tom et al.,

I know there has been a lot of discussion before about changing dice or how rolls are done. Some are complicated and some are not. Some get rid of too much luck and some aren't a large improvement, and most are hard for people to understand.

I wanted to throw and idea out there called Run it Twice Rolling. The basic idea is that each roll is done normally and works for all types of dice rolls, attack bonuses and defense bonuses all work. To explain more easily let me start with an example. Let's say that Player A has 7 and Player B is defending with 3.

Roll 1:

Player A: 5 4 2

Player B: 3 2

Result: Player A kills 2

Roll 2:

Player A: 5 5 2

Player B: 5 4

Result: 1 and 1

Roll 3:

Player A: 5 2 1

Player B: 5 1

Result: 1 and 1

Roll Result:

Player A loses 1

Player B loses 1

Even though in the first roll Player A kills 2 it isn't the result until we get the same result twice. So in this case it went 1 and 1 on roll 2 and then again on roll 3, so the result is a 1 and 1 loss. Had in roll 2 Player A killed 2 then the result of the turn would have been Player A killing 2.

The end result of rolling this way is that some of the variance is removed from the games. It also should be easy for almost everyone to understand and could be turned on as an option in any game that has dice.

Comments?

Sounds simple to understand (which I'm a big fan of)...but I call upon the power of the math gurus to know if it would actually make a difference!  

Very interesting idea. I am pretty sure it would indeed reduce the variance.

Hi GP - I thought this would work. I am somewhat surprised at the results. Just for convenient notation, I'll list the probabilities in the order DefenderLoses2-Split-AttackerLoses2. The usual 6-sided dice have probabilities 0.372-0.336-0.293. The per-roll variance is 0.658.

Your procedure outputs 0.393-0.336-0.271. (fyi - the splits were different in the fourth digit, but rounded to 3 they are the same.) The per-roll variance is 0.649. The attacker enjoys a greater edge, which I think is counter to what you're trying to do. The slight variance reduction seems due to the shift.

Note that if we had 1/3-1/3-1/3 dice, the symmetry of the procedure would produce 1/3-1/3-1/3. Our even-ish die are somewhat close to that, and I think that's why it's not changing variance much.

so you're saying it doesn't work out correctly?

Yes, I am saying that. But I never want my posts to sound like, "It doesn't work. HUGH HAS SPOKEN!"

Surprising, I reckon. But what if you attack with 1 dice against 2 ?

Toto wrote:

Surprising, I reckon. But what if you attack with 1 dice against 2 ?

I'm going to make a rough estimate that 80%+ of attacks that occur are of the 3v2 variety, and that 1v2 attacks happen much less than 1% of the time, so though 1v2  stats may be relevant, they are not consequential.

Toto wrote:

Surprising, I reckon. But what if you attack with 1 dice against 2 ?

Or 3v1/2v1/1v1: You'd be going from 2 outcomes to 2 outcomes, so you'd either be changing the mean or using the same dice. My impression of the goal is to keep the mean the same while reducing variance.

With three outcomes, this is possible. For example, if the die were perfectly even at .33-.33-.33, you could reduce variance by making the die .25-.50-.25 or .1-.8-.1. (In a nutshell, we'd want more splits without changing the edge. Whatever edge exists can be kept be evenly contributing from the lose 2's towards the splits.)

It wont work.

KNOSKEN HAS SPOKEN!